Question

Bob flips a coin 3 times.
Let A be the event that Bob flips Heads on the first two flips.
Let B be the event that Bob flips Tails on the third flip.
Let C be the event that Bob flips Heads an odd number of times.
Let D be the event that Bob flips Heads at least one time.
Let E be the event that Bob flips Tails at least one time.
(a) Determine whether A and B are independent.
(b) Determine whether A and C are independent. (When computing P(C) don’t forget to account for orderings!)
(c) Determine whether A, B, and C are independent.
(d) Determine whether A and D are independent.
(e) Determine whether D and E are independent.
HINT: In this problem justify your answer by computing the appropriate probabilities. Recall that events F and G are independent if P(F G) = P(F)P(G).

Answer 1